Breather excitations in the sine-Gordon equation influenced by constant driving forces are investigated—large driving forces cause the breather to split into a $k\bar{k}(2\mathrm{}\pi \mathrm{kink}-2\mathrm{}\pi \mathrm{antikink})$ pair while for small driving forces the breather excitations enter stationary modes. A perturbation method and a potential-energy argument yields expressions for the threshold for breather decomposition. Good agreement between theory and numerical results is found when the initial phase ($\theta$) of the breather is either 0 or $\pi$. For $\theta \cong \frac{\pi }{2}$ and $\theta \cong \frac{3\pi }{2}$ the deviation gets larger.

A consistent description of the spin-glass transition and the spin-glass phase is possible within the context of equilibrium statistical mechanics. This conclusion is based on two arguments. First, every equilibrium state may be decomposed uniquely into its ergodic components, which represent the pure thermodynamic phases. Second, all the ergodic components have the same free energy. A detailed analysis of the ensuing conceptual structure is given and its agreement with experiments on field-cooled spin-glasses is pointed out.

The merging of a large system of parallel Rayleigh-Bénard rolls with a plane boundary is investigated. Close to the threshold of the instability a variational formulation exists in the amplitude approximation. It is shown that the optimal angle of the rolls with the normal boundary is $0.63{\epsilon }^{\frac{1}{4}}$ where the small number $\epsilon$ is the difference between the actual Rayleigh number and its value at the threshold of linear stability.

Relaxation and fluctuations of nonlinear macroscopic systems, which are frequently described by means of Fokker-Planck or Langevin equations, are studied on the basis of a master equation. The problem of an approximate Fokker-Planck modeling of the dynamics is investigated. A new Fokker-Planck modeling is presented which is superior to the conventional method based on the truncated Kramers-Moyal expansion. The new approach is shown to give the correct transition rates between deterministically stable states, while the conventional method overestimates these rates. An application to the Schlögl models for first- and second-order nonequilibrium phase transitions is given.

An echo has been observed in the fine-structure quantum beats of a coherently excited collection of sodium high-Rydberg-state atoms. This echo may be of value in the study of collisional dephasing of Rydberg-state atoms in much the same way as spin echoes and photon echoes have been used to study relaxation processes in other systems.

In thermal-energy collisions between sodium atoms in $\mathrm{ns}$ or $\mathrm{np}$ states ($32<~n<~52$) and xenon atoms, depopulation of the Rydberg states is observed to occur predominantly through state-changing reactions of the type $\mathrm{Na}(ns or np)+\mathrm{Xe}\to \mathrm{Na}(n-1, l>~2)+\mathrm{Xe}$. For the present range of $n$, the measured cross sections increase with $n$ and lie between 1500 and 2600 ${\mathrm{\AA }}^2$ for $\mathrm{ns}$ states and between 2000 and 4200 ${\mathrm{\AA }}^2$ for $\mathrm{np}$ states. Implications of the data are discussed.

Recently a method was formulated for treating electron scattering from a potential in a rather strong laser field. The method has now been applied to the case of a local Gaussian potential. The results, reported on here, provide a test of the applicability of the Kroll-Watson soft-photon approximation. This approximation appears to be surprisingly accurate over the range of frequencies and field strengths considered.

The whole-atom integral incoherent-scattering cross sections of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$ $\gamma$ rays of energy 1170 and 1330 keV in 38 elements have been obtained from the measured total attenuation cross sections of their compounds with the use of the mixture rule and the graphical extrapolation method reported earlier by the authors. The results are discussed.

An explanation is proposed for the increase in the width of the band of allowed states near threshold found in recent experiments by Cannell, Dominguez-Lerma, and Ahlers on wave-number selection in a Taylor-Couette system. A simple parametrization of the forcing of the motion by the nonuniform gap between the cylinders used to yield the selection produces many features of the data.

Diffusion of a particle in the quadratic bistable potential $V\left(x\right)=\frac{1}{2}k{\mathrm{}\left(\right|x|-1\mathrm{})\mathrm{}}^2$ and the $n$-dimensional double well with $n\gg 1$ is examined in the limit of small noise. We obtain exact closed-form expressions for the probability distribution valid for all times.

It is found that nonlinear coupling of whistler waves with ion-cyclotron fluctuations can lead to spiky whistler electric field envelopes. Analytical results for the latter, which are solutions with discontinuous derivatives, are given. Possible application of our results in solar-wind plasmas is discussed.

We have used the Kanai Hamiltonian, for a quantum-mechanical particle experiencing frictional interactions with its environment, to calculate the influence of dissipation in the surroundings on quantum-mechanical tunneling. We find that for the case of a rectangular potential-energy barrier, the dissipation can either increase or decrease the transmission coefficient, depending on the magnitude of the barrier height and width.

The adiabatic-nuclei theory, which is widely used in electron-molecule scattering calculations of cross sections for nuclear excitation, is known to be invalid near threshold. A new "scaling procedure" for correcting the adiabatic-nuclei theory for rotational excitation is introduced and applied to $e$-${\mathrm{H}}_2$ collisions in the rigid-rotor approximation. At near-threshold energies, the resulting cross sections are shown to be in very good agreement with accurate laboratory-frame close-coupling results.

Triple-differential cross sections for the ionization of helium by 500-eV electrons at small momentum transfer have been analyzed in terms of the exchange of one single virtual photon between the helium atom and the scattering electron. The helium form factor has been described by quantum-defect parameters. The variation of the asymmetric binary-recoil angular distributions (i) with the momentum transfer in the collision, and (ii) with the energy of the ejected electron have been obtained in good agreement with experiment. Previous theoretical work seems to suffer primarily from precision in the target wave functions.

Cavity degenerate-parametric-amplifier and cavity four-wave-mixing configurations capable of producing a large amount of squeezing near the threshold of oscillation are discussed. Cavities allow one to reduce the pump power delivered to the gain medium, or to select a gain medium which has less gain per unit length, but may be better suited for squeezed-state production in other respects.

The electron density in the high-temperature microplasma region of a titanium vacuum spark discharge is measured from the relative intensities of the dielectronic satellites of the Ti xii resonance line. The triplet doubly excited levels $2s2p{}_{}{}^3{}_{}{}^{}P$ and ${2p}^2{}_{}{}^3{}_{}{}^{}P$ of Ti xii are populated primarily by inner-shell excitation due to energetic electron impact, and the resulting triplet satellite lines are enhanced relative to the singlet satellite lines. The measured electron density in the microplasma region is 1.5×${10}^{23}$ ${\mathrm{cm}}^{-3\mathrm{}}$. This represents an energy concentration of ${10}^8$ J ${\mathrm{cm}}^{-3\mathrm{}}$ and a plasma kinetic pressure of ${10}^9$ bars.

The self-diffusion constant vanishes in a scattering medium approaching a percolation transition, and the shear viscosity diverges near a glass transition. If the dependence of these transport coefficients upon the distance to the transition point $\epsilon$ and upon the frequency $\omega$ is given by a scaling law, it is shown that the "long-time tails" on the correlation functions, whose time integrals give the transport coefficients, diverge. The divergences are expressed in terms of existing critical exponents only. The theory is in reasonable agreement with existing experimental results and with related theories.

A general class of Hamiltonian systems is studied in which neighboring phase-space islands are shifted in phase. This leads to reconnection of Kolmogorov-Arnold-Moser level curves and necessitates a reexamination of the island overlap criterion for the breakdown of adiabatic barriers between island chains. An analytic reconnection threshold is derived from an averaged Hamiltonian and found to agree closely with numerical surfaces of section for a model mapping. Numerous applications to physical problems are indicated.

The problems encountered in the channel-coupling array (CCA) calculations of the preceding paper, viz., the failure to achieve convergence and the persistence of unphysical potential-energy curves, are resolved herein with the use of the ${\mathrm{H}}_2^{+}$ ion as a test case. Convergence is obtained by the use of local interpolates and the finite-element method in place of the globally defined, LCAO-type (linear combination of atomic orbitals) functions previously used. Physically correct, ungerade potential-energy curves result from calculations in which the ungerade CCA channel component wave functions are each required to vanish on the midplane normal to the symmetry axis, just like the solution to the Schrödinger equation. A proof of the foregoing property plus detailed discussions of the finite-element method and its CCA and Schrödinger-equation solutions, of spurious solutions, of convergence, and of implications of the calculations are presented.

The linear coupled-cluster method and a hierarchy of its approximations are employed to investigate the Slater $X\alpha$ method and to study the exchange-correlation effects in the beryllium atom. An analysis of the various contributions to the exchange-correlation corrections to the total energy is made using the approximations to the coupled-cluster model. The total dominance of the valenceshell exchange-correlation corrections, the role of the single-particle excitation terms, and the relative importance of the ring- and ladder-diagram terms are gleaned from these calculations. The exchange parameter $\alpha$, for the calculation of the reference state, i.e., the $X\alpha$ orbitals, is chosen using the criterion that the total energy computed by the $X\alpha$ method be equal to the Hartree-Fock total energy for the atom. For this reference state, the total energy of the beryllium atom, with the inclusion of the exchange-correlation correction, is found to be - 14.663 598 hartrees, a value very close to the experimental energy of - 14.669 hartress. The $X\alpha$ method is seen to provide good single-particle reference states for many-body calculations.